LONDON (Reuters) - Global oil supply could fall in line with demand more quickly if OPEC and Russia agree to a steep enough cut in production, but it is unclear how rapidly this might happen, the International Energy Agency said on Tuesday.

OPEC, led by Saudi Arabia, agreed last month to cut production to around 32.5 to 33 million barrels per day (bpd) and Russia has signaled it is ready to join in any effort to temper supply and shrink a stubborn global surplus of unwanted crude.

Oversupply helped send oil prices from $115 a barrel in June 2014 to as low as $27 in January this year. Crude has since recovered to around $50 on expectations of a production cut.

The IEA said in its August report it expected world oil demand to grow at a rate of 1.2 million bpd next year, keeping its forecast unchanged from last month, but cut its estimate of growth in 2016 by 40,000 bpd to around 1.2 million bpd, from around 1.3 million bpd last month.

"Even with tentative signs that bulging inventories are starting to decline, our supply-demand outlook suggests that the market -- if left to its own devices -- may remain in oversupply through the first half of next year," the IEA said. "If OPEC sticks to its new target, the market's rebalancing could come faster."

"At this stage, it is difficult to assess how the OPEC supply cut, if enforced, will affect market balances," the agency added.

"A significant rebound in production from Libya and Nigeria and further growth from Iran would suggest that bigger cuts would have to be made by others, such as Saudi Arabia, to meet the ... production target."

OPEC members meet next month in Vienna.

Iran is recovering market share after years of Western sanctions, in Libya, civil unrest has cut production and a series of attacks on oil infrastructure have curtailed Nigerian supply.

All three are expected to be exempt from any coordinated cuts, meaning that the onus will likely rest on some of the higher-producing members, such as Saudi Arabia and Iraq.

The IEA forecast a decline of 900,000 bpd in non-OPEC output in 2016 to 56.6 million bpd, and expects a rise of 400,000 bpd in 2017.

Global stockpiles fell for the first time since March, down 10 million barrels to 3.092 billion barrels, just shy of July's record 3.111 billion barrels.

"The fall in stockpiles was largely driven by crude, which fell in all OECD regions and especially sharply in Asia Oceania. This brought crude stocks back to early February levels. Refined product stocks across the OECD hit yet another historic high as refineries increased runs in August," the IEA said.

The agency said global demand growth has continued to slow after hitting a five-year high of 2.5 million bpd in the third quarter of last year, to a four-year low of 800,000 bpd in the third quarter of this year, due to "...vanishing OECD growth and a marked deceleration in China."